Optomechanical Quantum Information Processing with Photons and Phonons

We describe how strong resonant interactions in multimode optomechanical systems can be used to induce controlled nonlinear couplings between single photons and phonons. Combined with linear mapping schemes between photons and phonons, these techniques provide a universal building block for various classical and quantum information processing applications. Our approach is especially suited for nano-optomechanical devices, where strong optomechanical interactions on a single photon level are within experimental reach.

Figure 1

(a) Setup of two tunnel-coupled OM crystal cavities (see Refs. 4, 13 for more details). (b) Level diagram showing the lowest mechanical and optical excitations in a two-mode OMS. Resonant coupling ($\delta =0$) occurs when the tunnel splitting $2J$ between the optical modes is comparable to the mechanical frequency ${\omega }_m$. (c) Different sets of strongly and weakly coupled optical modes and control laser fields can be used for nonlinear interactions (${\omega }_s$, ${\omega }_a$, ${\omega }_L$) and purely linear photon storage and retrieval operations (${\omega }_c^{\prime }$, ${\omega }_L^{\prime }$).

Figure 2

(a) Energy level diagram of a resonantly coupled OMS, $\delta =2J-{\omega }_m=0$, and for a single mechanical mode in the ground state. (b) Excitation spectrum and $g^{(2)}(0)$ for a weak coherent field exciting the $c_a$ mode, where $g_0/\kappa =8$ and $n_0={\Omega }_a^2/{\kappa }^2$. (c) Minimal value of $g^{(2)}(0)$ as a function of the OM coupling strength $g_0$ and for different values of $N_{\mathrm{th}}$. The analytical results (solid lines) given in the text are in good agreement with the exact numerics (circles). The dashed line shows the asymptotic scaling $\sim 8{\kappa }^2/g_0^2$ at zero temperature.

Figure 3

A single-phonon single-photon transistor. (a) An incoming photon in port (A) passes through the interferometric setup and leaves through port (A) or (B), depending on the phase shift $\Delta \varphi$ acquired upon reflection from the two-mode OMS. (b), (c) For a mechanical system in state $|0_m⟩$, the OMS exhibits a single resonance at ${\omega }_s$ ($\Delta \varphi =\pi$), while for state $|1_m⟩$, the resonance splits by $g_0\gg \kappa$ and the photon does not enter the cavity ($\Delta \varphi =0$).

Figure 4

(a) OM quantum memory, where “path-encoded” photonic qubits are stored in long-lived mechanical states using tunable linearized OM interactions $\sim {\Omega }_i^{\prime }(t)$. Deterministic gate operation between stationary qubits are implemented by a controlled phonon-phonon interaction $\sim {\Omega }_s(t)$ as described in the text. (b) The total error ${ϵ}_g$ for implementing a controlled phase gate between two phononic qubits is minimized with respect to ${\Delta }_s$ and plotted as a function of $\kappa$ and ${\Gamma }_m$ (see text). The parameters for this plot are $g_0/(2\pi )=50\mathrm{MHz}$, $\gamma /(2\pi )=4\mathrm{kHz}$, $\alpha =1$, and $g_0/\delta =1/3$.